Solve for $x$ and $y$ using elimination. ${-5x-y = -23}$ ${-4x+y = -4}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-9x = -27$ $\dfrac{-9x}{{-9}} = \dfrac{-27}{{-9}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-5x-y = -23}\thinspace$ to find $y$ ${-5}{(3)}{ - y = -23}$ $-15-y = -23$ $-15{+15} - y = -23{+15}$ $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-4x+y = -4}\thinspace$ and get the same answer for $y$ : ${-4}{(3)}{ + y = -4}$ ${y = 8}$